Problem: You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

Solution (in PYTHON3):

Solution:
import sys
from sys import stdin

tt = 1

for loop in range(tt):

    a,b,k = map(int,stdin.readline().split())

    if k == 0:
        print ("Yes")
        print ("1"*b + "0"*a)
        print ("1"*b + "0"*a)

    elif a == 0:
        if k > 0:
            print ("No")
        else:
            print ("Yes")
            print ("1"*b)
            print ("1"*b)

    elif a+b-1 <= k:
        print ("No")

    else:
        

        x = [None] * (a+b)
        y = [None] * (a+b)

        x[k] = "1"
        y[k] = "0"
        x[0] = "0"
        y[0] = "1"

        a -= 1
        b -= 1

        for i in range(len(x)):
            if x[i] != None:
                continue
            if a > 0:
                x[i] = "0"
                y[i] = "0"
                a -= 1
            else:
                x[i] = "1"
                y[i] = "1"

        x.reverse()
        y.reverse()

        
        x = "".join(x)
        y = "".join(y)

        if x[0] == y[0] == "1":
            print ("Yes")
            print (x)
            print (y)
        else:
            print ("No")